One who fights over secretary's shredder output (5,5)
I believe the answer is:
scrap paper
'shredder output' is the definition.
'one who fights over secretary's' is the wordplay.
'one who fights' becomes 'scrapper'.
'over' is an insertion indicator.
'secretary' becomes 'pa' (I've seen this in other clues).
'scrapper' placed around 'pa' is 'SCRAP PAPER'.
(Other definitions for scrap paper that I've seen before include "somewhere to make notes" , "What shamefaced News International decided to do" , "Make jottings on this!" .)